Prove the theorem of the broken chord (if AB and BC make up a broken
chord in a circle, where BC is greater than AB, and if M is the midpoint
of arc ABC, the foot F of the perpendicular from M on BC is the midpoint
of the broken chord).

A teacher's textbook, and his colleagues, all assume that if two geometric objects have
different tick marks, then the two angles or segments indicated must be incongruent.
Doctor Peterson unpacks the ambiguity, then warns against the larger error of reading
too much in sketches.

Two circles intersect such that their centers and their points of
intersection form a square with each side equal to 3. What is the total
area of the sections of the square that are not shared by both circles?